The Whatever@example.com Solution

Solution (sort of): Well, you could tell these folks to use a fake email address. Anything at example.com would do: qwerty@example.com, 123@example.com, etc. Once or twice each day, you would then go to http://yoursite/moodle/admin/user.php and confirm the new accounts. This is not a perfect solution, but it will certainly work for you and your users.

Temporary Email

Another way to go: Use a temporary email service like this one: http://10minutemail.com/. There are many others. This will allow your students to quickly confirm their accounts and start Moodling.